Largely, as it would seem,[516] through Schulze, whose _Erläuterungen_ did much to spread Kant’s teaching, this view came to be the current understanding of Kant’s position. The nature of arithmetic, as thus popularly interpreted, is expounded by Schopenhauer in the following terms: “In time every moment is conditioned by the preceding. The ground of existence, as law of the sequence, is thus simple, because time has only one dimension, and no manifoldness of relations can be possible in it. Every moment is conditioned by the preceding; only through the latter can we attain to the former; only because the latter was, and has elapsed, does the former now exist. All counting rests upon this nexus of the parts of time; its words merely serve to mark the single steps of the succession. This is true of the whole of arithmetic, which throughout teaches nothing but the methodical abbreviations of counting. Every number presupposes the preceding numbers as grounds of its existence; I can only reach them through all the preceding, and only by means of this insight into the ground of its existence do I know that, where ten are, there are also eight, six, four.”[517] Schulze was at once challenged to show that this was really Kant’s teaching, and the passage which he cited was Kant’s definition of the schema of number, above quoted.[518] It is therefore advisable that we should briefly discuss the many difficulties which this passage involves. What does Kant mean by asserting that in the apprehension of number we generate time? Does he merely mean that time is required for the process of counting? Counting is a process through which numerical relations are discovered; and it undoubtedly occupies time. But so do all processes of apprehension, in the study of geometry no less than of arithmetic. That this is not Kant’s meaning, and that it is not even what Schulze, notwithstanding his seemingly explicit mode of statement, intends to assert, is clearly shown by a letter written by Kant to Schulze in November 1788. Schulze, it appears, had spoken of this very matter. “_Time, as you justly remark, has no influence upon the properties of numbers_ (as pure determinations of quantity), such as it may have upon the nature of those changes (of quantity) which are possible only in connection with a specific property of inner sense and its form (time). _The science of number, notwithstanding the succession which every construction of quantity demands, is a pure intellectual synthesis which we represent to ourselves in thought._ But so far as _quanta_ are to be numerically determined, they must be given to us in such a way that we can apprehend their intuition in successive order, and such that their _apprehension_ can be subject to time....”[519]